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3 years ago

If you help me with this fast I will brain you. Thanks.

Mathematics

1 answer:

irakobra [83]3 years ago

5 0

Answer:

-2 and -6 is the correct answer

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Help me answer this question

Allushta [10]

Use the formula a^2+b^2=c^ which is 7.21

3 0

3 years ago

Read 2 more answers

The graph 4x^2-4x-1 is shown. Use the grpah to find the estimates for the solutions of 4x^2-4x-1=0 and 4x^2 - 4x-1=2

Darina [25.2K]

Answer:

a) The estimates for the solutions of $4\cdot x^{2}-4\cdot x -1 = 0$ are $x_{1}\approx -0.25$ and $x_{2} \approx 1.25$ .

b) The estimates for the solutions of $4\cdot x^{2}-4\cdot x -1 = 2$ are $x_{1}\approx -0.5$ and $x_{2} \approx 1.5$

Step-by-step explanation:

From image we get a graphical representation of the second-order polynomial $y = 4\cdot x^{2}-4\cdot x -1$ , where $x$ is related to the horizontal axis of the Cartesian plane, whereas $y$ is related to the vertical axis of this plane. Now we proceed to estimate the solutions for each case:

a) $4\cdot x^{2}-4\cdot x -1 = 0$

There are two approximate solutions according to the graph, which are marked by red circles in the image attached below:

$x_{1}\approx -0.25$ , $x_{2} \approx 1.25$

b) $4\cdot x^{2}-4\cdot x -1 = 2$

There are two approximate solutions according to the graph, which are marked by red circles in the image attached below:

$x_{1}\approx -0.5$ , $x_{2} \approx 1.5$

5 0

3 years ago

Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$

Applying condition: y'(0)=0, we get $0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}$

Therefore,

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

3 0

3 years ago

What survival rate in the 10th year would make the average of loss over the 10 year period equal to 38.0%

Marat540 [252]

Answer: 63%

Step-by-step explanation:

<u>First step</u>

Find the 10th year rate of loss that will make the average of loss over the 10 years to equal 38.0%.

Assume this rate is x;

$\frac{(36.2 + 29.0 + 46.2 + 37.5 + 40.9 + 40.0 + 32.6 + 40.5 + 40.1 + x)}{10} = 38.0\\\\\frac{343 + x}{10} = 38\\\\x = 380 - 343\\\\x = 37$

x = 37%

<u>Second step - Survival rate</u>

The survival rate is calculated by;

= 1 - rate of loss

= 1 - 37%

= 63%

7 0

2 years ago

A customer purchases 10 m dade co. florida 7.50% g.o. bonds at a 9.50 basis. how much interest will she collect each year? $75 $

crimeas [40]

In the value of bonds, the symbol "M" means "thousands.
Therefore, 10 M = 10,000$

So, the customer bought a coupon with 10,000$ and the expected annual interest is 7.5% of the coupon's value.

Calculating the value of interest is simple, just multiply the interest rate (7.5%) by the original value of the coupon to know how much interest she will collect each year.

Interest collected each year = (7.5 / 100) x 1000 = 750$

5 0

3 years ago